Tuesday, August 12, 2014

One of the bigger long-running scandals in the economics scientific credit game has been the downgrading of the role of the late Lionel W. McKenzie in proving the existence of a competitive general equilibrium, generally credited to Arrow and Debreu. Roy Weintraub, who has championed McKenzie's cause for over 30 years, has a new book out with Till Duppe from Princeton University Press, _Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit_, which reveals fresh details about the matter. David Warsh at economics principals has written an interesting summary with solid background, with Mark Thoma also linking to Warsh's excellent account (sorry I am failing to get the direct link to Warsh's account working, titled "The Startling Story behind a Famous Footnote").

The big new news from this book is about the role of Debreu in delaying the publication of McKenzie's paper and also suppressing knowledge of it, particularly to his coauthor, Kenneth Arrow (who, arguably, should have found out about the paper on his own). McKenzie's paper was finished first and even though Debreu as referee for it at Econometrica delayed it, it actually came out one issue ahead of the slightly more general paper by Arrow and Debreu. McKenzie cited their paper, but theirs did not cite his, which had been presented a day before theirs at a 1952 Econometric Society conference, with Debreu attending McKenzie's talk, which Arrow did not do, and Debreu not tellling Arrow about it. Of these parties, only Arrow remains alive. BTW, while it may be less general, McKenzie's proof is quite a bit simpler and has shown up in some textbooks over the years.

Weintraub also reports that McKenzie long ago accepted that he was going to get less credit and be forgotten largely, taking a philosophical attitude and noting all the famous and deserving people who never got the Nobel Prize in their fields. More power to him on that, although one must feel sorry about the whole thing, with Weintraub attributing this to a "Matthew Effect" of who is already rich gets richer and who is poor gets poorer. Weintraub continues to campaign that general equilibrium should be called "Arrow-Debreu-McKenzie" (or ADM), but with only a few people following his advice on this, even though properly it should be called "McKenzie-Arrow-Debreu." This is definitely a case of somebody getting the shaft big time, although it is not the only such case out there, but then this is one of the most influential ideas in all of economics, so a pretty big deal.

I shall add an arguably irrelevant but ironic anecdote from personal experience about McKenzie and the economics Nobel. It dates to my first attendance at an AEA meeting in Dec. 1973 in New York. I remember that I was in an elevator in the Hilton and was randomly in there with Lionel McKenzie (I saw his name badge) and somebody else I did not recognize the name of. I knew of McKenzie and even at that time about how he had gotten screwed over on this matter. He and his companion were discussing the economics Nobel (please, no comments on how it is really the Swedish Bank Prize, I know, I know), and I note that this was just four years after the prize had been established. Most of the "big trees in the forest" had not yet gotten it, although Arrow had, shared inappropriately with Hicks, so the fix was already in regarding what would happen to McKenzie (Debreu got it later by himself).

So, McKenzie argued to his friend that the next recipient would be Joan Robinson, and that the committee would give it to her for her 1933 book, _The Economics of Imperfect Competition_, which would certainly have been a justifiable award. He then rather sarcastically commented that he expected her to reject the award for not being for her later work, leading to the two of them laughing quite a bit, although as far as I was concerned she also deserved it for her later work as well. That was it as they then left the elevator. Of course, neither Robinson nor McKenzie ever got the award, but I have always heard that she did not get it partly because of her politics and partly because of their fear that she would engage in some combative misbehavior from their perspective.

McKenzie: "IN THE PAST few years several writers have presented sets of postulates for an abstract market and then proved that the market has a position which satisfies conditions of competitive equilibrium..."

I read this as proving the "existence" of competitive equilibrium for an abstract market as postulated by the economist/mathematicians. How does that differ from "proving the existence" of vampires in the novel Dracula by Bram Stoker?

Good one, Peter. GET MAD indeed. And we can get even too, while we are at it, :-).

BTW, Joan Robinson died in 1983, only 10 years after that conversation I overheard happened, while McKenzie only died in 2010, well into his 80s. Lots of people have complained about her not getting the Prize, but far fewer have about McKenzie. I saw him talk a few years before his death, and he seeemed like someone who was satisfied with his life and circumstances, an elegant man with a dry wit.

Speaking of people being satisfied or not with themselves, I once met Robin Williams, in Siena of all places. He was quiet and nice and smiling, but it is curious that at the time I had this strong sense that he was not happy and that the smile was a facade. Oh well, we never know who is happy and who is not, and if McKenzie was satisfied despite getting jerked around, good for him.

In the 70's, a group of us young 'uns were discussing with one of our professors, a former colleague of Debreu. One of us suggested how Robinson should get it. To which he snapped back: "She is not one of us.We will never allow this!"

I remember an anecdote about Joan Robinson, who had spent some time dealing with mental health issues (depression, if memory serves). She apparently said (perhaps more than once) that she was the only British economist who has a certificate attesting to sanity.

I regret that I never met Joan Robinson, in contrast to all the others in this tale. But I have heard a lot of anecdotes regarding her eccentricities (some of which Don Coffin might have heard also when we were in grad school together), but I am not going to propound any further here. However, some of them were pretty bizarre, and I am not surprised that she suffered depression and got some certificate certifying she was sane. However, her rep and her very radical (Maoist) politics for a period of time (apparently stepped away from at the end of her life) all conspired to keep her from the Prize.

I will add one anecdote that is not so much about her, but more about those making these decisions. I have heard it from a primary source that Assar Lindbeck, the longtime dominant personality on the econ Nobel committee, once said that there were two people who would get the prize over his dead body: Joan Robinson and James Buchanan, although why he apparently did not say at that time. She died in 1983, but Buchanan got the prize in 1986, with Lindbeck still the dominant figure and not dying as a result. Maybe if she had lived a bit longer...

S-man. It is a math theorem. If you want to argue that it has no relevance to the real world, be my guest. Assumptions are made, equilbrium is defined in a certain way, and then it is proven that with the right assumptions, there can be an equilibrium as defined. These proofs, certainly the classic ones, all involve fixed point theorems.

There are multiple ways to critique this, if you want to. One is to do a Velupillai and question deeper underlying axioms of math itself, such as the Axiom of Choice or the Law of the Excluded Middle, which are generally just assumed without anybody even thinking about them. However, if they are not true, then it becomes much harder to prove existence of equilibrium from the usual assumptions. The fixed point theorems do not work the same way in constructivist math.

The other way to go, which I think is what you are more into, is to simply argue that these theorems are irrelevant to actually existing economies; they are too abstract, or whatever.

No, Barkley, I don't want to argue that it has no relevance to the real world. I don't know that it has none. I also don't know that it has any relevance.

What I do want to argue, though, is for the importance of distinguishing between a formal proof of a abstract math theorem and some sort of evidence (which this presumably isn't) that something akin to competitive equilibrium exists in real economies.

Here's my concern. I assume that Arrow-Debreu is legit, but considering what O. F. Hamouda refers to as "the flippant way in economics in which consensuses are formed to become the truth," how do I know that somebody riffing off Arrow-Debreu isn't just blowing smoke out their pie-hole?

The Keynesians mangle Keynes. The Marxists mangle Marx. But I'm supposed to assume that the mathematicians are airtight just because they like to use the word "rigor" self-referentially? No, I don't think so.

Well, this is a sideshow from the main point of the post, which was really about the sociology of the discipline rather than the nature of the theorem itself, which is a long long issue and one I have written about extensively. Rather than just blowing you or anybody else following this off, let me make just a few remarks, and that will be all I have to say here. Any further comments from me will be "go read my stuff."

So, in fact it does look to me that your main point really is the one about real world relevance, which is a legitimate issue to raise. I will first note one area where supposed GET gets used where it is ridiculous, and that is in the macro DSGE models. These models get defended partly because they supposedly have this wonderful micro foundation in GET. This is just garbage of a very high order, and while he has been polite about it, Arrow has made this clear on several occasions.

Regarding real world existence of general competitive equilibrium, it has probably never existed anywhere ever, or if it has, it has been for one second while all markets were equilibrated, before at least one of them slipped out of equilibrium yet again. OTOH, lots of partial equilibria exist out there much of the time in many individual markets, many of which work fairly well in that narrowly defined sense: equilibrium is unique and quite stable. But then there are others, some of them quite important, where things are not so well behaved (go read my stuff for lots of discussion of such cases).

One defense of GET, and this is one reason why I think it is worth teaching it at a sufficiently high level in econ ed, is that there is some correspondence between the conditions for existence and whether or not markets "work well" in the real world. So, one must have competition, full information, and complete markets, this latter ruling out both externalities and "public goods" (more properly, collective consumption goods). And, guess what, in the real world we see markets not behaving well when there is monopoly power, asymmetric information, unresolved externalities, and public goods. If there is a real world app of GET, it may be in highlighting how these work.

That said, there are other sources of problems with GET beyond the mere existence issue. These include both uniqueness and stability, and these problems were recognized by the more serious GE theorists, not to mention such goodies as the SMD theorem, which connects with those. As I think you know, S-man, I am very much a student of complex nonlinear economic dynamics, which I think is very relevant to the real world, and much of that arises from precisely these latter sorts of failures that are not tied to the basic existence theorems.

There are of course all sorts of real world problems that GET simply does not address directly, such as income distribution. But, again, this is well understood by the theorists of these matters. Distribution is essentially assumed up front and so not really explained. GET does not remotely explain everything.

Well said, Barkley. The only part that stumps me is how what you just said above is a "sideshow" from the sociology of the discipline. Not crediting people for the priority of work they have done is another symptom of the same "flippancy" as using the results of the work inappropriately or simply misrepresenting it.

Let me say that there are all kinds of issues about whether or not existence of GE is an important or relevant or useful result, and I only barely scratched the surface above. However, whether or not it is (and why it is or is not) does not change the fact that the vast majority of economists think that it is an important, with many thnking it is the most important theorem of economics (usually in conjunction with the First Welfare Theorem that says GE is Pareto optimal), and this is not going to change no matter what you or I say here. It will continue to be taught to grad students, even in het grad programs, although more critically in those than others.

So, the sociology issue, and why Roy Weintraub in particular has spent so much time worrying about this, has to do with who gets credit for this result that is so widely known and taught. That really is a separate issue from the details of the result or whether it really deserves all the attention it gets or not. The discussion is about how more powerful individuals (Debreu in particular) jerk around less powerful ones (McKenzie) in the professions.

Let me add that this is not really about the ideologies of the personalities involved either. This was the case with Joan Robinson, where it has been widely believed that her heterodox radicalism was a factor (along with her acerbic personality) in her not receiving the Nobel, even as such people as McKenzie thought she deserved it from nearly the beginning of the prize.

McKenzie was not any heterodox or radical, indeed was pretty pro-free market, near as I can tell. In my tale about him and Robinson, he was making fun of her later more heterodox views and saying she deserved the prize for her earlier more standard stuff on imperfect competition. He ended up at the University of Rochester, which dept he more or less controlled for decades, with David Warsh comparing his role there to Samuelson's at MIT after Harvard refused to hire him due to anti-Semitism (McKenzie had job market problems and problems getting his PhD approved).

The Rochester dept under his influence became a fairly free market-oriented one, and in more rcent years has housed some of the advocates of the obnoxiously silly DSGE approach. He was pretty old by this time and perhaps not running things by then, but it may be that he supported this stuff. I do not know. His technical work in growth theory was always very elegant, and he was more open to some interesting ideas, such as not forbidding negative prices in general equilibrium, which was a big issue that the more standard approaches spent huge amounts of time fussing over (cannot have negative prices! even though we see them in the real world...).

Indeed, if anything Arrow certainly was more leftist in politics and ideology than McKenzie, openly declaring his "socialist sympathies" at various points, which I do not think McKenzie particularly had. Arrow, of course, has long been completely aware of the many limittions of general equilibrium theory, which is one of the reasons he was the main economist involved in the founding of the Santa Fe Institute.

The large review book on General Equilibrium by Ingrao and Israel around '90(its history, with many details, was reviewed in Am Ma Mo. and it paraphrased its conclusion as 'it exists, but hardly ever, and maybe never can you find it, and can't ever if you relax the conditions' (but it was better said)---and that doesnt even deal with the SMD criqtique, though the book does (which is quite good and only somewhat technically detailed).

I think GET can be looked at like the integers or rational numbers---when considering the reals, they have a measure 0 in, say, the unit interval. Nonetheless, people use them all the time---i rarely have to wait at the store when my change turns out to be a transcendental number---they just truncate the weight of my vegetables to the nearest $100 (though its bounded below by 100. I sometimes use the 0 argument to say stuff like when i went to india and they said i had to have 1000$ in cash, i said i had 2000 (but i didnt mention thats if you count in 1/10 of a penny. Or, if you owe me 1$, why not pay me 100$ because 0s dont add value.

I do agree DSGE has nothing or little to do with GET---its an approximation. However, people often use approximations such as discretizing equations to simulate them (leading to issues like is 'chaos just an epiphenomenon due to computer roundoff error'. (god made the integers, all else is human error or sin---euler). One reason GET is essentially as ideal a model as the ideal gas (which doesn't explain phase transitions, origin of life, etc.) is because real life transactions are 'quantized' or discrete---there is friction, frustration (as in spin glasses, ramsey's theorem etc.) The amount of confusion (in my view) on these topics in the academic literature is quite impressive. (Like group selection in biology). But, some people still think Iraq didn't have WMD, not realize that actually its been verified that 'Paul McCartney is dead (1968)' or that the faked moon landing by NASA caused the global warming hoax. (see Lewendowsky (joseduarte.com )for example on how you can make statistics lie---to your financial benefit , and lies propogate (PNAS June 2014)). 'if you can give me 4 parameters, i can fit your data to an elephant, and 1 more i'll make its ears wiggle' (n Wiener---had one of the original 'classical diffusion' approaches to quantum theory) around 31).

Regarding credit, I still haven't got a prize or credit for for my earlier discovery of the "participatory Economics' (parecon) of Hahnel (emeretis of AU and Albert of Zmag). my family invented this before in a simple form---you put a sheet of paper on the refrigerator, and list a set of tasks, and then negotiate who does what (dishes, trash, sweeping etc.) . This is called a balanced job complex. (I was excused because i am 'specially abled' even if i believe in the golden rule (also called US constitution)---from each according to ability, to each according to need' (i am disabled, need everything and can do nothing) plus they had no check off for 'theory' 'speculation' or philosophy'; chores are not my field, and below the pay grade of my balanced job complex. as voltarie put it, all men are equal (dictatorship of the proletariat), but somebody else has to work the fields.